Hi guys. I'm just starting to work with Lebesgue integrals, and so even the easy stuff is awkward for me.
EDIT: Okay, I cracked it. Here's my solution, for reference purposes:Quote:
Let be a nonnegative measurable function. Show that implies almost everywhere (i.e. except on a set of measure zero).
Let denote the domain of , and put for each positive integer and . Then is measurable, and so by prop. 4.12 of Royden, Real Analysis 3rd Ed (p87), . Thus we have for all , which means and therefore . The conclusion follows.